Inference for Two Lomax Populations Under Joint Type-II Censoring

TL;DR

This paper develops and compares statistical inference methods for Lomax distributions under joint type-II censoring, including EM, Bayesian, and bootstrap techniques, with applications to real bladder cancer data.

Contribution

It introduces EM and Bayesian estimation procedures for Lomax distributions under joint censoring, addressing convergence issues of Newton-Raphson and providing comprehensive performance comparisons.

Findings

EM algorithm performs well in estimation accuracy.

Bayesian methods yield credible intervals with good coverage.

Simulation results compare various confidence interval methods.

Abstract

Lomax distribution has been widely used in economics, business and actuarial sciences. Due to its importance, we consider the statistical inference of this model under joint type-II censoring scenario. In order to estimate the parameters, we derive the Newton-Raphson(NR) procedure and we observe that most of the times in the simulation NR algorithm does not converge. Consequently, we make use of the expectation-maximization (EM) algorithm. Moreover, Bayesian estimations are also provided based on squared error, linear-exponential and generalized entropy loss functions together with the importance sampling method due to the structure of posterior density function. In the sequel, we perform a Monte Carlo simulation experiment to compare the performances of the listed methods. Mean squared error values, averages of estimated values as well as coverage probabilities and average interval lengths are considered to compare the performances of different methods. The approximate confidence intervals, bootstrap-p and bootstrap-t confidence intervals are computed for EM estimations. Also, Bayesian coverage probabilities and credible intervals are obtained. Finally, we consider the Bladder Cancer data to illustrate the applicability of the methods covered in the paper.